The cubic-tetragonal (c-t) two-phase equilibria in ZrO_2-CeO_2 and ZrO_2-R_2O_3 (R : rare earths) systems and related phenomena were examined. The results obtained are summarized as follows.(1) The c-t transformation in near-stoichiometric ZrO_2-CeO_2 is regarded as a second-order phase transition.(2) In nonstoichiometric (Zr, Ce) O_2-x, -oxygen ions are regularly displaced in the <111> direction in a cubic form. A variety of forbidden reflections appear in the diffraction patterns by the displacement in cubic fluorite structure.(3) The c-t transformation in nonstoichiometric (Zr, Ce) O_2-x has a nature of first-order phase transition.(4) The c-t two-phase field in ZrO_2-R_2O_3 systems is dependent on the type of R^<3+> ions. Thermodynamic assessment is successful to describe the observed two-phase fields in vaious ZrO_2-R_2O_3 systems on the assumption that the c-t transformation is of a second-order type.(5) It is possible to obtain ZrO_2-ZrN solid solutions by mechanical alloyins,